[Toán 8] khó

P

perfectday8

$ \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 2 \leftrightarrow z = \frac{xy}{2xy - (x+y)} $
z nguyên $ \rightarrow xy $ \geq $ 2xy - (x+y) \leftrightarrow x + y $ \geq $xy$
$ \leftrightarrow x = 1 \ (1) \vee y = 1 \ (2) \vee x = y = 2 \rightarrow z = 1 \ (3) $
(3) thỏa.
$ (1) \leftrightarrow \frac{y+z}{yz} = 1 \leftrightarrow y = z = 2. \\
S = \{ 1,2,2 \}. $
 
You must log in or register to reply here.
Top Bottom